Systems with More Than One Degree of Freedom

  • Ahmed A. Shabana
Part of the Mechanical Engineering Series book series (MES)


Thus far, the theory of vibration of damped and undamped single degree of freedom systems was considered. Both free and forced motions of such systems were discussed and the governing differential equations and their solutions were obtained. Basic concepts and definitions, which are fundamental in understanding the vibration of single degree of freedom systems, were introduced. It is the purpose of this chapter to generalize the analytical development presented in the preceding chapters to the case in which the systems have more than one degree of freedom. We will start with the free and forced vibrations of both damped and undamped two degree of freedom systems.


  1. Shabana AA (1997) Vibration of discrete and continuous systems. Springer, New YorkGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Ahmed A. Shabana
    • 1
  1. 1.Richard and Loan Hill, Professor of Engineering, Department of Mechanical & Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

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